Merry-go-round modeled as a solid disk of mass M=100kg and radius R=2.0 m is rot
ID: 2099321 • Letter: M
Question
Merry-go-round modeled as a solid disk of mass M=100kg and radius R=2.0 m is rotating in a horizontal plane about a frictionless vertical axle. A student with mass 240kg standing on the rim of the merry-go-round while it is rotating at angular speed of 4.00 rad/sec. Now student start to walk slowly from the edge toward the center.
(Moment of inertia (I) for a solid disk is 0.5MR^2 and I for a point mass at a distance R from a rotating axis is MR^2)
A) Find the moment of inertia of the system (student + disk) before student starts to walk towards the center.
B) Find the total angular momentum of the system before student starts to walk towards the center.
C) Find the new moment of inertia of the system when she reaches a point 0.6m from the center
D) Now find the new angular speed of the system when she reaches a point 0.6m from the center.
E) Find the work done on the student as she walks to r=0.6 meters
F) Explain why the angular momentum of the above system is conserved when student walks toward the center.
Explanation / Answer
M= 100kg, r=2m ,m=240 kg, w= 4rad/s a). I= Mr^2/2 +mr^2 =1160 kg-m2 b). L = I*w = 4640 kg-m2/s c). I' = 0.5Mr^2 +m(0.6)^2 = 286.4 kg-m2 d). I'w' = Iw => 286.4 *w' = 1160* 4 => w' = 16.2 rad/s e). W = 1/2 I'w'^2 -1/2 Iw^2 => W= 28301.4 J f). because no external torque is acting on the system